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A functional equation - kobi_78 - 07/05/2010

Hi,

Does anyone have an idea how to solve the following functional equation?

Thanks




RE: A functional equation - 73939 - 07/08/2010


Let's start there. Then, we plug in 1 to get . Then .


RE: A functional equation - bo198214 - 07/08/2010

(07/05/2010, 07:28 PM)kobi_78 Wrote: Hi,

Does anyone have an idea how to solve the following functional equation?

Thanks


Thats called "Julia equation", generally
f(F(x))=F'(x)f(x) to solve for f.

You obtain an Abel function from it, or obtain it from an Abel function via:


you can solve it at a fixed point via comparing the powerseries coefficients.